<i>L</i>1-Regularization Path Algorithm for Generalized Linear Models

TLDR

L1 regularization selects variables by penalizing the L1‑norm of coefficients, offering a less greedy alternative to forward–backward selection. The study introduces a path‑following algorithm for L1‑regularized generalized linear models. The algorithm efficiently computes solutions along the entire regularization path using a predictor–corrector convex‑optimization method, with step‑length strategies to control accuracy. The algorithm was validated on simulated and real datasets.

Abstract

Summary We introduce a path following algorithm for L1-regularized generalized linear models. The L1-regularization procedure is useful especially because it, in effect, selects variables according to the amount of penalization on the L1-norm of the coefficients, in a manner that is less greedy than forward selection–backward deletion. The generalized linear model path algorithm efficiently computes solutions along the entire regularization path by using the predictor–corrector method of convex optimization. Selecting the step length of the regularization parameter is critical in controlling the overall accuracy of the paths; we suggest intuitive and flexible strategies for choosing appropriate values. We demonstrate the implementation with several simulated and real data sets.